Question

Integrate with respect to x :
∫1−36x2−5x+2dx
84
48
-84
-48
Integrate with respect to v :
∫104v−632v2dv
8
58
−85
85

Answer 1

Answer on Question #51611 – Math – Integral Calculus

Integrate with respect to $x$: $\int (1 - 36x^2 - 5x + 2)dx$

Solution:

$$\begin{array}{l} \int (1 - 36x^2 - 5x + 2)dx = \int 1dx - \int 36x^2 dx - \int 5xdx + \int 2dx = \\ = x - 36 \cdot \frac{x^3}{3} - 5 \frac{x^2}{2} + 2x + C = 3x - 12x^3 - \frac{5}{2}x^2 + C \end{array}$$

where $C$ is an arbitrary real constant.

Integrate with respect to $v$: $\int (104v - 632v^2)dv$

Solution:

$$\int (104v - 632v^2)dv = \int 104vdv - \int 632v^2dv = 104 \frac{v^2}{2} - 632 \frac{v^3}{3} + C = 52v^2 - \frac{632}{3}v^3 + C$$

where $C$ is an arbitrary real constant.

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